A second order \(\eta \)-approximation method for constrained optimization problems involving second order invex functions. (English) Zbl 1212.90307

Summary: A new approach for obtaining second order sufficient conditions for nonlinear mathematical programming problems which makes use of the second order derivative is presented. In the so-called second order \(\eta \)-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order \(\eta \)-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order \(\eta \)-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.


90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
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